And to stress, in my experience the ultra-competitiveness belongs to a small minority. Most people in West London are pretty sane - though I am not sure whether the rest of the country would agree.
For me part of the problem is that in order to work out a path through, eg to identify the one aspirational, two realistic and one fall back school, which will suit your child you inevitably turn to playground gossip, or indeed Mumsnet, on top of the schools own marketing. Its slightly easier if your child is already at a prep or a state primary with a strong track record of sending children to these schools. Unfortunately those most likely to have that information are those who have put the most research in, and thus most likely to be ahead of the game in tutoring etc.
Another problem, though at times an advantage, is the astonishing multi-national nature of these schools' west London catchments. Everyone brings something to the party, and my own DC, despite being born and schooled within a mile or two of where their grandfather was born and schooled, have a much more international outlook and greater aspirations that they might have done had they been raised elsewhere. Some of their friend's parents (Russian, American, Lebanese, Chinese, Italian etc) confirm they are staying in London primarily for the education.
However there are disadvantages when other people's priorities and values clash with those you want for your children. In our shabby middle class way we want our children to believe in society and accept that success brings responsibility, which does not always line up with some of the winner takes all approaches elsewhere. As above I hate being quizzed about my daughter's exams marks by the mother desperate to work out where her child stands, in a school keen to discourage this sort of overt competition. For me education, including resilience and roundedness should take priority over just grades. Success surely is about becoming a good, emotionally intelligent adult, not just about earning more than everyone else.
I hate also the overbearing sense of entitlement that some, say mega-successful financiers and their wives, seem to possess. It is as if as Schmetz suggests, they see their children's achievements reflecting upon their own. They can also appear to expect that their wealth should guarantee them the best of everything. So if you run some City institution your child must also be a top dog and go to SPGS. Some is overt, but there is also a certain joy in spotting the well hidden surprise when one of these uber-successful people realises that your child goes to a school they are aspiring to even though you are just very ordinary Brit, who only just merits a basic level of acknowledgement.
I liked the expat banker's wife who was surprised to discover that in her DD's year at SPGS there were some DC who had been to state primaries, and who had made it without paying all those fees and without agonising over which of several very similar central London preps gave her DD the best chance of getting in. I liked it less when my DD, aged 13 was approached by another girl in my hearing and asked how she had done in the Junior maths challenge and when DD replied "Gold" the other girl said "How come, you only go to such and such school, and that is not supposed to be as academic as .." and she went on to list some of the other alternatives. God knows what happens when these kids leave their rarified Chelsea lives. I assume that Ivy League offers a better chance of remaining in the bubble than even Oxford.
That said and as DC move towards tertiary education, it is becoming clear that maths geeks are set to inherit the world. Places at Cambridge, LSE, Imperial, and Warwick for subjects like engineering or economics are now dependent on serious maths qualifications. Often Step 2, rather than just A*. So perhaps all that Kumon and tutoring was the way forward, and DC will need to retrain as plumbers to service the homes of the new Masters of the Universe.